Factor the following expression: $5$ $x^2+$ $19$ $x$ $-30$
This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(5)}{(-30)} &=& -150 \\ {a} + {b} &=& & & {19} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-150$ and add them together. Remember, since $-150$ is negative, one of the factors must be negative. The factors that add up to ${19}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-6}$ and ${b}$ is ${25}$ $ \begin{eqnarray} {ab} &=& ({-6})({25}) &=& -150 \\ {a} + {b} &=& {-6} + {25} &=& 19 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {5}x^2 {-6}x +{25}x {-30} $ Group the terms so that there is a common factor in each group: $ ({5}x^2 {-6}x) + ({25}x {-30}) $ Factor out the common factors: $ x(5x - 6) + 5(5x - 6) $ Notice how $(5x - 6)$ has become a common factor. Factor this out to find the answer. $(5x - 6)(x + 5)$